Answer: 1.)
A. 30in^2
B. 18cm^2
C. 130yd^2
2.) The formula for the area of a triangle is half the base times the height. So 1/2 x 40 x 32 = 640cm^2
3.) 17 yards. The fence that enclose Sondra's backyard is a right triangle whose sides measuring 8 yards, 15 yards and 17 yards respectively.
4.) From the Pythagorean Theorem we know:
hypotenuse^2 = side^2 + side^2
hypotenuse^2 = 36 + 36
hypotenuse = square root (72)
hypotenuse = 8.48528... feet
5.) a. 5
b. √128
c. √221
Area of triangle are [tex]30inches^{2}[/tex] in part(a),
[tex]18[/tex] [tex]centimerters^{2}[/tex] in part(b) and [tex]130[/tex] [tex]yards^{2}[/tex] in part(c)
What is Triangle?
In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.
What is area?
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
According to questions, we have the following
In part (a.), h = [tex]6[/tex] inches; b = [tex]10[/tex] inches
In part (b.), h =[tex]9[/tex] centimeters; b =[tex]4[/tex] centimeters
In part (c.) h = [tex]13[/tex] yards; b = [tex]20[/tex] yards
We have to find the area of each triangle with the given heights and bases.
Now, Area of triangle in part a
[tex]=\frac{1}{2}[/tex]×[tex]b[/tex]×[tex]h[/tex]
[tex]=\frac{1}{2}[/tex]×[tex]6[/tex]×[tex]10[/tex]
[tex]=30inches^{2}[/tex]
Area of triangle in part b
[tex]=\frac{1}{2}[/tex]×[tex]9[/tex]×[tex]4[/tex]
[tex]=18[/tex] [tex]centimerters^{2}[/tex]
Area of triangle in part c
[tex]=\frac{1}{2}[/tex]×[tex]13[/tex]×[tex]20[/tex]
[tex]=130[/tex] [tex]yards^{2}[/tex]
Hence, we can conclude that area of triangle are [tex]30inches^{2}[/tex] in part(a),
[tex]18[/tex] [tex]centimerters^{2}[/tex] in part(b) and [tex]130[/tex] [tex]yards^{2}[/tex] in part(c)
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What is the slope of the line that is perpendicular to the line whose equation is 2x + y = 4.
Answer:
The slope of the line that is perpendicular to the line whose equation is 2x + y = 4 is [tex]\frac{1}{2}[/tex].
Step-by-step explanation:
Given : Equation is 2x + y = 4.
To find : What is the slope of the line that is perpendicular to the line.
Formula used : equation of line y = m[tex]m_{1}[/tex] x + c.
Solution : We have 2x + y = 4.
Rearranging the equation : y = - 2x + 4.
On comparing m[tex]m_{1}[/tex] = - 2.
Condition for slope of the line that is perpendicular to the line :
m[tex]m_{1}[/tex] × m[tex]m_{2}[/tex] = -1 .
So, -2 × m[tex]m_{2}[/tex] = -1 .
On dividing by 2 both we get ,
m[tex]m_{2}[/tex] = [tex]\frac{1}{2}[/tex].
Therefore, The slope of the line that is perpendicular to the line whose equation is 2x + y = 4 is [tex]\frac{1}{2}[/tex].
If the value of 2x3 is 2, then what is the value of x?
I'm not sure what this is exactly?
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -5 - 5 cos θ
Answer:
The graph of polar equation is symmetric about the x-axis.
Step-by-step explanation:
The given polar equation is
[tex]r=-5-5\cos \theta[/tex]
If [tex](r,\theta)[/tex] and [tex](r,-\theta)[/tex] lie on the graph then the graph of polar equation is symmetric about the x-axis.
Substitute [tex]\theta=-\theta[/tex] in the given equation.
[tex]r=-5-5\cos (-\theta)[/tex]
Cosine is an even function.
[tex]r=-5-5\cos \theta[/tex] [tex][\cos (-\theta)=\cos (\theta)][/tex]
Point [tex](r,-\theta)[/tex] lies on the graph, therefore the graph of polar equation is symmetric about the x-axis.
A skier is trying to decide whether whether or not to buy a season ski pass. A daily pass cost 67. A season ski pass costs 350. The skier would have to rent skis with either pass for 25 per day. How many days would the skier have to go skiing in order to make the season pass cost the same as the daily pass option.
Write an expression using words to represent the cost of a daily pass. Write the algebraic expression. Write an expression using words to represent the cost of a season pass. Write the algebraic expression
How can you compare the cost of a daily pass with the cost of a season pass algebraically?
which other angle must also measure 130°
opposite angles are identical so if angle 1 = 130
than angle 3 is also 130 degrees
Answer:
Angle 3
Step-by-step explanation:
we know that
[tex]m<1=m<3[/tex] -----> by vertical angles
we have
[tex]m<1=130\°[/tex]
therefore
[tex]m<3=130\°[/tex]
what is the area of a triangle that has a base of 8 yd and height of 3 yd
area = 1/2 x b x h
1/2 x 8 x 3 = 12
area is 12 square yards
What is the sum of the first five terms of a geometric series with a1 = 10 and r = 1/5?
Answer: 12.496
Step-by-step explanation:
The formula to find the sum of geometric progression is given by :-
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Given : The first term : [tex]a_1=10[/tex]
Common ratio = [tex]r=\dfrac{1}{5}=0.2[/tex]
Then , the sum of first five terms of a geometric series is given by :-
[tex]S_5=\dfrac{10(1-(0.2)^5)}{1-0.2}=12.496[/tex]
Hence, the sum of the first five terms of given geometric series =12.496
3 -1 ___ 1/4 which one is the correct answer.
=
<
>
3-1 = 2
2 is greater than 1/4
so > is the answer
Daria applied a transformation to triangle ABC to obtain triangle A′B′C′. The two triangles are not congruent. Which of the following could be the transformation Daria applied?
What is the quotient (3x3 + 10x2 + 10x + 4) ÷ (x + 2)?
a. 3x2 + 16x + 42
b. 3x2 + 4x + 2
c. 3x2 − 16x + 42
d. 3x2 − 4x + 2
Answer:
Option B is correct.
[tex]3x^2+4x+2[/tex].
Step-by-step explanation:
We are asked to find the quotient obtained by dividing the expression [tex](3x^3+10x^2+10x+4)[/tex] by the expression [tex](x+2)[/tex]
We can also write this expression as i.e. we are asked to find the value of the expression:
[tex]\dfrac{3x^3+10x^2+10x+4}{x+2}[/tex]
We can write the expression on the numerator as:
[tex]3x^3+10x^2+10x+4=(3x^2+4x+2)(x+2)[/tex]
Hence,
[tex]\dfrac{3x^3+10x^2+10x+4}{x+2}=\dfrac{(3x^2+4x+2)(x+2)}{x+2}[/tex].
Hence,
[tex]\dfrac{3x^3+10x^2+10x+4}{x+2}=3x^2+4x+2[/tex].
Hence, option B is correct.
Hence, the quotient is:
[tex]3x^2+4x+2[/tex].
I SERIOUSLY NEED HELP HERE!!!!!
PLEASE SOMEONE HELP ME ON THIS!!!!!
NEED MAJOR HELP HERE CALCULATOR QUIT ON ME!!!!!!!
scientific calculator of a TI83 or TI84 ( does that help?)
Use the data below to find the correlation coefficient. (Remember to choose DiagnosticOn on your calculator.)
x y
270 70
230 75
250 68
310 82
285 80
275 76
281 73
267 81
252 72
246 79
The correlation coefficient is _____. Round to the nearest thousandth.
THESE ARE MY OPTIONS:
a. 0.438
b. 0.192
c. 0.5
d. 0.720
A blimp is 1100 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. If those measurements are 75.2° and 17.9°, how far apart are the two stadiums?
The angle of depression represents the angle from a horizontal layout to a lower surface. The distance between the two stadiums is 3115.1 meters
The given parameters have been illustrated using the attached image of triangles.
The stadiums are represented with A and B.
First, calculate distance BO using:
[tex]\tan T =\frac{BO}{TO}[/tex]
Where:
[tex]\angle T = 90 -75.2 = 14.8[/tex]
[tex]TO = 1100[/tex]
So, we have:
[tex]\tan(14.8^o) = \frac{BO}{1100}[/tex]
Make BO the subject
[tex]BO = 1100 * \tan(14.8^o)[/tex]
[tex]BO = 1100 * 0.2642[/tex]
[tex]BO = 290.62[/tex]
Next, calculate distance AO using:
[tex]\tan T =\frac{AO}{TO}[/tex]
But in this case:
[tex]\angle T = 90 -17.9 = 72.1[/tex]
[tex]TO = 1100[/tex]
So, we have:
[tex]\tan(72.1^o) = \frac{AO}{1100}[/tex]
Make AO the subject
[tex]AO = 1100 * \tan(72.1^o)[/tex]
[tex]AO = 1100 * 3.0961[/tex]
[tex]AO = 3405.71[/tex]
The distance AB between the 2 stadiums is:
[tex]AB = AO - BO[/tex]
[tex]AB = 3405.71-290.61[/tex]
[tex]AB = 3115.1[/tex]
Hence, the distance between the 2 stadiums is 3115.1 meters.
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The equation of a line is 2(y+1)=10x+3
The y-intercept of the line is ___, and the slope of the line is ___.
Answer: The answer is 0.5 and 5.
Step-by-step explanation: The given equation of the line is
[tex]2(y+1)=10x+3.[/tex]
We are to find the y-intercept and the slope of the given line.
We know that the slope-intercept form of a line is given by
y = mx + c, where, 'm' is the slope and 'c' is the y-intercept of the line.
We have
[tex]2(y+1)=10x+3\\\\\Rightarrow 2y+2=10x+3\\\\\Rightarrow 2y=10x+3-2\\\\\Rightarrow 2y=10x+1\\\\\Rightarrow y=5x+0.5.[/tex]
Therefore, c = 0.5 and m = 5.
Thus, the y-intercept of the line is 0.5 and the slope is 5.
A sandwich shop offers ham, turkey, tuna, chicken salad, and roast beef. It has Swiss, American, and provolone cheese. You can order a sandwich on white, wheat, or rye bread. If a person orders a sandwich and chooses a meat, cheese, and bread at random, how many sandwich choices are there?
5 different meats
3 different cheeses
3 different breads
5x3x3 = 15*3 = 45
there are 45 choices
The sandwich shop offers a total of 45 different sandwich combinations based on the given options of meats, cheeses, and breads. Each sandwich consists of one type of each category.
Explanation:The question asked is related to the concept of combinations in mathematics. It gives a variety of choices for making a sandwich - 5 types of meats, 3 types of cheeses, and 3 types of breads. Assuming that each sandwich will have one meat, one cheese, and one type of bread, we can calculate the total combinations by multiplying the number of options in each category together. Combinations are used when the order of selection does not matter.
So, the total number of sandwich combinations would be 5 (meats) * 3 (cheeses) * 3 (breads) = 45 different sandwich choices.
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What is the area of the composite figure?
(6π + 4) cm2
(6π + 16) cm2
(12π + 4) cm2
(12π + 16) cm2
The area of the composite figure is 6π + 16 cm²
Composite Figure:Composite figures are composed of different dimensional figures. The area of a composite figure is the sum of the whole 2 dimensional figures that forms the composite figure.
Therefore, the figure above has 3 semi circle and 1 square.
Therefore, the area can be calculated as follows;
area = sum of the area of the 3 semi circle + area of the squarearea = 1 / 2 πr² + 1 / 2 πr² + 1 / 2 πr² + L²
area = 3 / 2 (πr²) + L²
where
r = 2 cm
L = 4 cm
Therefore,
area of the composite figure = 3 / 2(π × 4) + 4²
area of the composite figure = 3 / 2(4π) + 16
area of the composite figure = 6π + 16 cm²
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place a square on a coordinate graph and label each vertex with variables. prove that the diagonals of a square are congruent and perpendicular to each other.
Final answer:
To prove that the diagonals of a square are congruent and perpendicular, label the vertices of a square on a coordinate grid and calculate the slopes and lengths using the slope formula and distance formula respectively. The diagonals have slopes of +1 and -1, proving they are perpendicular, and they have equal lengths, proving they are congruent.
Explanation:
To prove that the diagonals of a square are congruent and perpendicular, we place a square with its vertices on a coordinate grid and label each vertex with variables.
Let's consider a unit square where c = 1 for simplicity, which means the length of each side is 1 unit. Place the square so that one vertex is at the origin (0,0), and label the vertices A(0,0), B(1,0), C(1,1), and D(0,1).
The diagonal AC will have endpoints at A(0,0) and C(1,1), and diagonal BD will have endpoints at B(1,0) and D(0,1). The slope of diagonal AC is (1 - 0)/(1 - 0) = 1, and the slope of diagonal BD is (1 - 0)/(0 - 1) = -1. Since the product of their slopes is -1 (1 * -1 = -1), this proves that they are perpendicular to each other.
To show they are congruent, we calculate their lengths using the distance formula: the distance between two points (x1,y1) and (x2,y2) is √[(x2 - x1)² + (y2 - y1)²]. Applying this to AC and BD reveals both lengths to be √[(1-0)² + (1-0)²] = √[1 + 1] = √2, proving the diagonals are congruent.
What number must be added to the expression below to complete the square?
x^2+3x
A. 9
B. 9/4
C. 3/2
D. 3
I think it is c or D but it should be C
hope that help
[I don't think it did lol ]
BMK
Can someone factor this problem for me?
Find the equation for the tangent line of f(x)=−3x2−7x+3 at x=3.
Linda is putting money into a savings account. She starts with $450 in the savings account, and each week she adds $70 .
Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Linda has been adding money. Write an equation relating S to W . Then use this equation to find the total amount of money in the savings account after 19 weeks.
If f(x) is an odd function, which statement about the graph of f(x) must be true?
It has rotational symmetry about the origin.
It has line symmetry about the line y = –x.
It has line symmetry about the y-axis.
It has line symmetry about the x-axis.
An odd function, by definition, is a function that is symmetric about the origin.
An even function, by definition, is a function that is symmetric with respect to the y-axis.
Since the question says that f(x) is an odd function, it has rotational symmetry about the origin. First option is correct.
ANSWER: symmetric about the origin.
Answer:It has rotational symmetry about the origin.
Step-by-step explanation:
An odd function : is a function that is symmetric about the origin.
An even function : is a function that is symmetric with respect to the y-axis.
Since , f(x) is an odd function, it has rotational symmetry about the origin.
its meaning that its graph remains unchanged after rotation of 180 degrees about the origin.
Therefore, It has rotational symmetry about the origin.
Temperature dropped from 11 below zero to 4 below zero how much did the temperature drop
Use the graph below to answer the following question:
graph of parabola going through negative 4, 4, negative 1, 5, and 1, negative 1
What is the average rate of change from x = –4 to x = 1?
–3
–1
0
1
Your answer should be
-1
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Multiply 3 [ 1 5 -5 6 0 0 ]
Simply multiply the number outside the brackets with each one inside it..
3 [ 1 5 -5 6 0 0 ]
3 x 1 = 3
3 x 5 = 15
3 x -5 = -15
3 x 6 = 18
3 x 0 = 0
3 x 0 = 0
[ 3 15 -15 18 0 0 ]
[ 3 15 ]
[ -15 18 ]
[ 0 0]
The answer is B and I hope I explained this well for you.
Carol spends 17 hours in a 2-week period practicing her culinary skills. How many hours does she practice in 5 weeks?
Final answer:
Carol practices for 8.5 hours per week, so in a 5-week period, she would practice for a total of 42.5 hours.
Explanation:
The student asked how many hours Carol practices her culinary skills in a 5-week period, if she practices for 17 hours in a 2-week period. To find the answer, we calculate how many hours Carol practices per week by dividing the total hours she practices in two weeks by two. Then we multiply the weekly hours by the number of weeks in question, which is five.
The calculation is as follows: Carol practices for 17 hours / 2 weeks = 8.5 hours per week. Then, 8.5 hours/week x 5 weeks = 42.5 hours in total for a 5-week period.
Can someone please explain me this
The length and width of a rectangle are 4.9^9 cm and 5.3^3 cm, respectively. What is the approximate area of the rectangle, using only positive exponents?
A) 5^6cm^2
B) 4^6cm^2
C) 5^12cm^2
D) 4^12cm^2
A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches. Find the area of the rectangle.
3 to the 2 over 3 power inches squared
3 to the 8 over 3 power inches squared
9 inches squared
9 to the 2 over 3 power inches squared
Answer:
9 square inches.
Step-by-step explanation:
We have been given that a rectangle has a length of the [tex]\sqrt[3]{81}[/tex] inches and a width of [tex]3^{\frac{2}{3}}[/tex] power inches. We are asked to find the area of given rectangle.
We know that area of rectangle in length times width of rectangle.
[tex]\text{Area of rectangle}=\sqrt[3]{81}\times 3^{\frac{2}{3}}[/tex]
We can write 81 as [tex]3^4[/tex] as:
[tex]\text{Area of rectangle}=\sqrt[3]{3^4}\times 3^{\frac{2}{3}}[/tex]
Using exponent rule [tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex], we can write [tex]\sqrt[3]{3^4}=3^{\frac{4}{3}}[/tex].
[tex]\text{Area of rectangle}=3^{\frac{4}{3}}\times 3^{\frac{2}{3}}[/tex]
Using exponent rule [tex]a^b\cdot a^c=a^{b+c}[/tex], we will get:
[tex]\text{Area of rectangle}=3^{\frac{4}{3}+\frac{2}{3}}[/tex]
[tex]\text{Area of rectangle}=3^{\frac{4+2}{3}}[/tex]
[tex]\text{Area of rectangle}=3^{\frac{6}{3}}[/tex]
[tex]\text{Area of rectangle}=3^{2}[/tex]
[tex]\text{Area of rectangle}=9[/tex]
Therefore, the area of given rectangle is 9 square inches.
evaluate 2^-3
No, there are no answer choices, but it has to be in fraction form.